1. Field of the Invention
This invention generally relates to a system for, and a method of, reducing deflections, vibrations and internal stresses in an upright structure, such as a high-rise, multi-floor building, exposed to external forces, such as earthquakes, winds and air bursts and, more particularly, to economically increasing the capability of the building from withstanding such disastrous conditions.
2. Description of the Related Art
It is known in the art of building construction to incorporate both active and passive dampers in a frame for absorbing deflections and vibrations caused by seismic disturbances. See, for example, U.S. Pat. Nos. 2,053,226; 3,418,768; 4,922,667; 5,065,552; 5,147,018; 5,152,110; 5,347,771; and 5,491,938.
FIG. 1 of the accompanying drawings is representative of such known frame constructions, wherein a high-rise, multi-floor building 10 is constructed of generally vertical columns 12 vertically stacked one above another, generally horizontal beams 14 connected to the columns in mutual parallelism, and dampers 16 mounted in generally diagonal damping braces 18. Each damper resembles an automobile shock absorber in that it typically consists of a piston slidable in a cylinder in which a viscous fluid, typically an inert operating fluid, such as silicone, is contained. Friction dampers could also be used.
As shown in FIG. 1, the building 10 is built on a foundation 20. Upon exposure to a seismic force, the building experiences deflections, vibrations and stresses. Each beam and column exhibits a localized flexing or bending movement or distortion. The damper absorbs energy as a function of the relative velocity and movement of the piston as dictated by the velocity and movement of the neighboring beams and columns.
A simplified model for each of the floors shown in FIG. 1 is depicted in FIG. 2, wherein F(t) represents the seismic force, and wherein springs 22 have been added to represent the effect of the axial flexibility of the stacked columns supporting the model at a level h above the ground 20. One of the nodes N has been separately identified to aid the following description.
The inter-story lateral displacement Ux and the lateral velocity Uxxe2x80x2 between the top and bottom of a column 12 are composed of two components. The first is based on the equivalent shear deformation (Uvx, Uxe2x80x2vx) i.e., local bending and shear deformation of the beams and columns, as well as the axial deformation of the diagonal damping braces. The second is based on the rocking component of deformation (Uax, Uxe2x80x2ax), i.e., the rotation created by the axial deformation of the stacked columns. This can be expressed by the following equations:
Ux=Uax+Uvxxe2x80x83xe2x80x83(1)
Uxe2x80x2x=Uxe2x80x2ax+Uxe2x80x2vxxe2x80x83xe2x80x83(2)
Only the equivalent shear components Uvx and Uxe2x80x2vx contribute to the displacement and the velocity of the damper 16. Thus, Uvx and Uxe2x80x2vx are derived from equations (1) and (2) as follows:
Uvx=Uxxe2x88x92Uaxxe2x80x83xe2x80x83(3)
Uxe2x80x2vx=Uxe2x80x2xxe2x88x92Uxe2x80x2axxe2x80x83xe2x80x83(4)
The effectiveness of the damper 16 is directly related to Uxe2x80x2vx and Uvx. As the contribution of Uxe2x80x2ax and Uax increases for a constant Ux and Uxe2x80x2x, the value of Uxe2x80x2vx and Uvx decreases. This effect is more pronounced at the upper levels of a high-rise building, where the axial deformation of the stacked columns is at its maximum. Thus, the effectiveness of the dampers is reduced at the upper levels of a high-rise building for a constant inter-story sway of the building.
The relationships above could also be explained by considering the angular rotation and velocity of the node N shown in FIG. 3. The damper force and absorbed energy are functions of the degree of distortion of the damping brace as shown in FIG. 3. The damping brace distortion could be measured by the internal angle xcex2 between the beam and column joining at node N. From FIG. 3, the following equations are obtained:
xcex1v+xcex2=90xc2x0xe2x80x83xe2x80x83(5)
xcex1v=xcex1xe2x88x92xcex1axe2x80x83xe2x80x83(6)
wherein xcex1 is the angular displacement of the column 12 from the vertical or rest position, wherein xcex1a is the angular displacement of the beam 14 from the horizontal or rest position, and wherein xcex1v is the measure of the distortion of the internal angle xcex2. These relationships are compared to this invention below.
It is the general object of this invention to protect a multi-floor, high-rise, building from external events, such as earthquakes, high winds, and air bursts by minimizing structural deflections caused by such events.
It is another object of this invention to retrofit existing buildings, or to build new buildings, with such protection.
It is still another object of this invention to protect occupants of such buildings from injury, especially in the case of seismic events.
In keeping with these objects and others which will become apparent hereinafter, one feature of this invention resides in coupling a damping system between a pair of upright truss systems that are spaced apart from each other. Each truss system has a truss column, a lower end region fixedly secured to the ground or foundation, and an upper free end region that is movable against resistance in a transverse oscillatory cantilever motion in response to external forces, such as seismic forces. Each truss system exhibits, as its dominant action, a cantilever movement against a rather significant structural resistance to lateral force.
In accordance with this invention, the effectiveness of the damping system is increased over prior art constructions by reversing the directions of the axial movement and velocity of the truss columns connected to the damping system. The damping system may, in a simple embodiment, include a single damper having opposite ends connected at nodes to the truss columns and movable relative to each other. During cantilever movement of one of the truss systems, the node connected to one of the damper ends moves in one direction, for example, upwardly, while the node connected to the other of the damper ends is connected to the other of the truss systems and moves in an opposite direction, i.e., downwardly. The axial deformation of the truss columns is enhanced over prior art constructions. This enhanced deformation causes the nodes connected to the columns to move through a longer relative distance and, in turn, a damper element of the damper to move through an enhanced working stroke.
In the preferred embodiment, each truss system includes, for each floor of the building, a pair of generally vertical, elongated columns, a pair of generally horizontal, elongated beams connected to the columns at corner regions, and a generally diagonal, elongated, stiffening brace connected at opposing corner regions to the columns and beams. Alternatively, or in addition, each truss system could include a solid wall of substantial width extending along the foundation, for example, a poured concrete wall extending over a substantial distance across the ground could exhibit the desired cantilever action according to this invention.
The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.